For questions 1-5 use the random variable X with values x = 2, 3, 4, 5 or 6 with P(x) = 0.05x.

1. Determine P (x = 4).

a. 0.05 b. 0.10 c. 0.15 d. 0.20

2. Find P (x >= 4).

a. 0.60 b. 0.45 c. 0.75 d. 0.55

3. What is P (2 < x <= 5)?

a. 0.70 b. 0.60 c. 0.45 d. 0.35

4. Give E (x).

a. 4.5 b. 4.75 c. 4.25 d. 5

5. Calculate sigma*x (note: see attachment).

a. 1.75 b. 2.121 c. 1.323 d. 3.063

For questions 6-10 use a binomial random variable X with n = 5 and p = 0.4.

6. Calculate the probability that x equals three.

a. 0.40 b. 0.913 c. 0.064 d. 0.2304

7. Determine the probability that x is at most two.

a. 0.337 b. 0.6826 c. 0.913 d. 0.317

8. Find the probability that x is at least two.

a. 0.0778 b. 0.663 c. 0.3370 d. 0.6826

9. What is the expected value of x?

a. 2 b. 2.5 c. 1.75 d. 2.25

10. Give the standard deviation of x.

a. 1.44 b. 1.09545 c. 1.2 d. 1

For questions 11-15 use a normal random variable X with mean sixty and standard deviation six.

11. Calculate the Z-score for x = 52.

a. 1.33 b. 0.4082 c. -1.33 d. 0.0918

12. Determine the value of x that is equivalent to a Z-score of 1.96.

a. 71.76 b. 61.96 c. 48.24 d. 76.71

13. Find the probability that x is between forty-five and seventy.

a. 0.9587 b. 0.0062 c. 0.0537 d. 0.9463

14. Give the probability that x is at most 78.5.

a. 0.999 b. 0.4990 c. 3.08 d. 0.001

15. What is the value of x such that P (X < x) is 0.3264?

a. -0.45 b. 57.3 c. 62.7 d. 0.45

1. Suppose that for a 5-year-old automobile, the probability the engine will need repair in year 6 is 0.3, while the probability that the tires need replacing in year 6 is 0.8. The probability that both the engine will need repair and the tires will need replacing in year 6 is 0.2. What is the probability that the tires will need to be replaced and the engine will need repair?

ANSWER AND EXPLANATION

2. Suppose that for a 5 year old automobile, the probability the engine will need repair in year 6 is 0.3, while the probability that the tires need replacing in year 6 is 0.8. The probability that both the engine will need repair and the tires will need replacing in year 6 is 0.2. If it is known that the tires will need replacing, what is the probability that the engine needs repair?

ANSWER AND EXPLANATION

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